Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+8y &= 2 \\ 4x+9y &= 5\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $4x = -9y+5$ Divide both sides by $4$ to isolate $x$ $x = {-\dfrac{9}{4}y + \dfrac{5}{4}}$ Substitute this expression for $x$ in the first equation. $-5({-\dfrac{9}{4}y + \dfrac{5}{4}}) + 8y = 2$ $\dfrac{45}{4}y - \dfrac{25}{4} + 8y = 2$ Simplify by combining terms, then solve for $y$ $\dfrac{77}{4}y - \dfrac{25}{4} = 2$ $\dfrac{77}{4}y = \dfrac{33}{4}$ $y = \dfrac{3}{7}$ Substitute $\dfrac{3}{7}$ for $y$ in the top equation. $-5x+8( \dfrac{3}{7}) = 2$ $-5x+\dfrac{24}{7} = 2$ $-5x = -\dfrac{10}{7}$ $x = \dfrac{2}{7}$ The solution is $\enspace x = \dfrac{2}{7}, \enspace y = \dfrac{3}{7}$.